Bayesian Inverse Problems

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Overview

Bayesian inverse problems use prior knowledge and measurement models to recover hidden images, fields, or physical parameters, while representing ambiguity with a posterior distribution. Common approaches include MCMC and variational inference, simulation-based inference, surrogate forward models, and learned priors based on diffusion models, normalizing flows, or neural operators. Applications range from MRI and image restoration to seismic tomography and PDE-constrained inference, where computation can be costly and the posterior may be high-dimensional or multimodal. A central challenge is making inference faster without sacrificing calibrated uncertainty: good measurement fit or reconstruction scores alone do not ensure that posterior samples capture the right spread and plausible alternatives.

Latest papers

CardsList

120 papers19 papers in the last four weeks, up 111% on the four weeks before. 0.1% of all new papers.

  1. Operator-Aware Posterior Sampling for Multivariate Weather Downscaling

    Oct 29, 2026Carlo Saccardi, Rudolf Saathof, Geethu Joseph +1Climate DownscalingDiffusion Posterior Sampling

    Delft University of Technology, The Netherlands

  2. Bayesian Inference of Expensive Simulators: Survey and Comparison of Design Choices

    Oct 27, 2026Šimon Soldát, Václav ŠmídlSimulation-Based InferenceBayesian Inverse Problems

    Department of Computer Science, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo náměstí 13, Praha 2, 120 00, Czech Republic.

  3. Image Modeling: From Handcrafted Priors to Foundation Image Models

    Oct 27, 2026A. Murat TekalpImage Inverse ProblemsConditional Generative Modeling

    Department of Electrical and Electronics Engineering, Koc¸ University, Istanbul, Turkey

  4. Exact Spectral Uncertainty Decomposition for Linear-Gaussian Bayesian M/EEG Inverse Problems

    Oct 21, 2026Ismail Huseynov, Stefan HaufeUncertainty QuantificationUncertainty Decomposition

    Physikalisch-Technische Bundesanstalt, Berlin, Germany · Technische Universitat Berlin, Berlin, Germany · Charité–Universitätsmedizin Berlin, Berlin, Germany

  5. Compositional neural networks for multimodal X-ray and neutron scattering inversion

    Oct 21, 2026Valentin Munteanu, Alexander Hinderhofer, Dmitry Lapkin +2Inverse ProblemsUncertainty-Aware Multimodal Fusion

    Institute of Applied Physics, University of Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany · Cluster of Excellence ”Machine Learning” - new perspectives for science, University of Tübingen, Germany

  6. Diffusion Posterior Sampling with Uncertain Forward Models

    Oct 21, 2026Wentao Shangguan, Vivek K GoyalDiffusion-Based Inverse ProblemsDiffusion Posterior Sampling

    Department of Electrical and Computer Engineering, Boston University, Boston, MA 02215, USA

  7. Predicting silent failures of learned inference under restricted access: what measurement physics and prior information explain

    Oct 20, 2026Mario GianniInverse ProblemsBayesian Inverse Problems

    School of Computer Science and Informatics, University of Liverpool, UK

  8. Hilbert-Scale Stability of Posterior Diffusion Priors for Ill-Posed Signal Recovery

    Oct 19, 2026Bahman Moraffah, Raha MoraffahDiffusion-Based Inverse ProblemsDiffusion Posterior Sampling

    Department of Computer Science, Data Science, and Artificial Intelligence, Worcester Polytechnic Institute

  9. Latent Annealed Posterior Sampling with a Variance-Preserving Bridge for Sparsely Observed Random Fields

    Oct 14, 2026Jiankun Lei, Tian QiPosterior SamplingBayesian Inverse Problems

    School of Statistics and Mathematics, Yunnan University of Finance and Economics, No. 237 Longquan Road, Wuhua District, Kunming, 650221, Yunnan, China

  10. Structure-aware Bayesian full waveform inversion via diffusion-regularized Stein variational gradient descent

    Oct 13, 2026Chao Li, Mrinal K. Sen, Sergey Fomel +1Seismic ImagingBayesian Inverse Problems

    The University of Texas at Austin

  11. Spanning Diffusion and Flow-based Posterior Sampling via Exact Gaussian Conditioning

    Oct 9, 2026Teo Deveney, Lea Bogensperger, Hok Shing WongPosterior SamplingDiffusion Posterior Sampling

    University of Bath · University of Zurich · LMU Munich

  12. Uncovering and Fixing Collider Bias in Bayesian PINNs

    Oct 8, 2026Michael Obermayr, Robert PeharzPhysics-Informed MLBayesian Inverse Problems

    TU Graz

  13. Kinetic Langevin Meets Split Gibbs: Accelerated Posterior Sampling for Imaging Inverse Problems with Diffusion Priors

    Oct 7, 2026Dai Hai Nguyen, Duc Dung NguyenBayesian Inverse ProblemsMarkov Chain Monte Carlo

    Hokkaido University · Institute of Information Technology, VAST

  14. Self-attention summary networks for subsurface velocity-model building from common-image gathers

    Oct 7, 2026Shiqin Zeng, Yunlin Zeng, Abhinav Prakash Gahlot +2Seismic ImagingInverse Problems

    Georgia Institute of Technology

  15. Twist Flow for Inverse Problems

    Oct 7, 2026Shiqin Zeng, Zijun Deng, Felix J. HerrmannBayesian Inverse ProblemsPosterior Sampling

    Georgia Institute of Technology

  16. Latent Score-Based Bayesian Cramér-Rao Bound Estimation for High-Dimensional Imaging Systems

    Oct 2, 2026Evan Scope Crafts, Thomas Wynn, Seonyeong Park +2Photoacoustic TomographyBayesian Inverse Problems

    Oden Institute for Computational Engineering and Sciences, the University of Texas at Austin, Austin, TX, 78712 · Graduate School of Biomedical Sciences at UT Southwestern Medical Center · Mallinckrodt Institute of Radiology at Washington University in St. Louis +1

  17. Deep Bayesian REFoCUS

    Oct 2, 2026Simon Penninga, Ruud van SlounUltrasound ImagingBayesian Inverse Problems

    Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

  18. Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems

    Oct 1, 2026Jan Blechschmidt, Oliver G. Ernst, Moritz Poguntke +1Posterior SamplingBayesian Inverse Problems

  19. BAM! Bayesian Anything Model: a foundation model for generative computational imaging

    Sep 30, 2026Alessio Spagnoletti, Charlesquin Kemajou Mbakam, Jonathan Spence +2Physics-Informed Generative ModelingPhysics-Guided Image Restoration

    Laboratoire MAP5, UMR 8145, Université Paris Cité, CNRS · Heriot-Watt University, School of Mathematical and Computer Sciences & Maxwell Institute for Mathematical Sciences

  20. A Missing Latent, Not a Missing Simulator: Radius-Augmented Inference for Real JWST Retrieval

    Sep 30, 2026Angshuman Chakravertty, P V V RajSimulation-Based InferenceBayesian Inverse Problems

    SVKM’s NMIMS (Deemed to be University)

  21. Principled MAP estimation for inverse problems: bridging the gap between convergence and performance

    Sep 29, 2026Alexandre Lagier, Valentine Tosel, Anne Gagneux +2Bayesian Inverse ProblemsBayesian Inference

    ENS de Lyon, CNRS, Université Claude Bernard Lyon 1, Inria, LIP UMR 5668, 69342 Lyon Cedex 07, France · Univ. Bordeaux, Inria, Bordeaux INP, IMB, UMR 5251, F-33400 Talence, France · Inria, ENS de Lyon, CNRS, Université Claude Bernard Lyon 1, LIP UMR 5668, 69342 Lyon Cedex 07, France

  22. Simulation-Based Inference for Plate Reverb System Identification

    Sep 28, 2026Dylan Sechet, Marc Evrard, Matthieu KowalskiParameter EstimationBayesian Inverse Problems

    Laboratoire Interdisciplinaire des Sciences du Numérique Université Paris-Saclay, Inria, CNRS, CentraleSupélec

  23. Generative Priors Conditioned on Natural Language for Bayesian Inversion in PDEs

    Sep 26, 2026Pengyu Zhang, Mark Girolami, Arnaud VadeboncoeurBayesian Inverse ProblemsConditional Generative Modeling

    Department of Engineering University of Cambridge Cambridge, CB3 0FA, UK

  24. FB-GDM: Fully-Bayesian Guided Diffusion Models for High-Dimensional Linear Inverse Problems via Unsupervised Variational Inference

    Sep 24, 2026Gatien Séguy, Thomas RodetDiffusion Model GuidanceBayesian Inverse Problems

    SATIE

  25. Generative Atmospheric Super-Resolution from Heterogeneous In Situ Observations through Composable Interfaces

    Sep 24, 2026Yang Xu, Dibyajyoti Chakraborty, Haiwen Guan +2Bayesian Inverse ProblemsData Assimilation

    School of Mechanical Engineering, Purdue University, West Lafayette, Indiana, USA · College of Information Sciences and Technology, The Pennsylvania State University, University Park, Pennsylvania, USA

  26. Variational objectives for amortized Bayesian inference in inverse problems: The role of posterior conditioning

    Sep 21, 2026Abhishek Srivastava, Arijit Hazra, Rajesh DubbakuAmortized InferenceBayesian Inverse Problems

    Department of Mechanical Engineering, Indian Institute of Technology Palakkad · Department of Mathematics, Indian Institute of Technology Palakkad

  27. PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers

    Sep 17, 2026Jiachen Yao, Zi-Siang Hsu, Xi Deng +5Uncertainty QuantificationBayesian Inverse Problems

    California Institute of Technology · National Taiwan University · Lawrence Berkeley National Laboratory +3

  28. Closed-form Bayesian homography estimation from noisy point correspondences

    Sep 14, 2026Hanne Beuter, Sebastian DornMulti-View GeometryUncertainty Quantification

    Technische Hochschule Augsburg · TTZ Landsberg am Lech · Augsburg, Germany

  29. Evaluation of optimisation and Bayesian inference methods for reaction rates in atmospheric chemical mechanisms

    Sep 13, 2026Valery Ashu, Wenqing Peng, Zhi-Song Liu +7Parameter EstimationBayesian Inverse Problems

    Department of Computational Engineering, LUT University, 15210, Lahti, Finland · Atmospheric Modelling Center-Lahti, 15140, 15140, Lahti, Finland · Institute for Atmospheric and Earth System Research / Physics, Faculty of Science, University of Helsinki, 00014, Helsinki, Finland +2

  30. Neural Posterior Estimation for Tomographic Weak Lensing Mass Mapping

    Sep 7, 2026Tim White, Shreyas Chandrashekaran, Camille Avestruz +2Neural Posterior EstimationBayesian Inverse Problems

    Department of Statistics, University of Michigan · Department of Computer Science and Engineering, University of Michigan · Department of Physics, University of Michigan